Résumé : In this talk, I will give an overview of our works on multiple scattering of interacting bosons in random media. Starting first with the non-interacting case, the effects of coherent backscattering and weak localization are introduced as the main interference corrections to diffusive transport in weak disorder. Then, I will extend the underlying theoretical concepts (ladder and crossed diagrams) to the case of many interacting particles (beyond the mean field approximation), and derive nonlinear transport equations which finally characterize the effect of interactions on diffusive transport and coherent backscattering. Furthermore, I will show that, by combining many-particle transport theory with quantum optical methods, our theory is also able to describe multiple scattering of intense laser light by dilute clouds of cold atoms.

Résumé : As recently discovered [1], Anderson localization (AL) in a bulk disordered system triggers the emergence of a coherent forward scattering (CFS) peak in momentum space, which twins the well-known coherent backscattering (CBS) peak observed in weak localization experiments. Going beyond the perturbative regime, we address here the long-time dynamics of the CFS peak in a 1D and 2D random systems [2]. Focusing on the 2D case, we show that CFS generally arises due the confinement of the wave in a finite region of space, and explain under which conditions it can be seen as a genuine signature of AL. In the localization regime, our numerical results show that the dynamics of the CFS peak is governed by the level repulsion between localized states, with a time scale related to the Heisenberg time. This is in perfect agreement with recent findings based on the nonlinear sigma model. In the stationary regime, the width of the CFS peak in momentum space is inversely proportional to the localization length, reflecting the exponential decay of the eigenfunctions in real space, while its height is exactly twice the background, reflecting the Poisson statistical properties of the eigenfunctions.

Résumé : In this talk I will discuss the dynamics of interacting
fermionic systems in the mean-field regime. Compared to the bosonic case,
fermionic mean-field scaling is naturally coupled with a semiclassical
scaling, making the analysis more involved. From a physical point of view,
as the number of particles grows one expects the quantum evolution of the
system to be effectively described by Hartree-Fock theory. The next degree
of approximation is provided by a classical effective dynamics,
corresponding to the Vlasov equation.
I will consider initial data which are close to quasi-free states, both at
zero and at positive temperature, with an appropriate semiclassical
structure. Under some regularity assumptions on the interaction potential I
will show that the time evolution of such initial data stays close to a
quasi-free state, with reduced one-particle density matrix given by the
solution of the time-dependent Hartree-Fock equation. The result holds for
all (semiclassical) times, and gives effective bounds on the rate of
convergence towards the Hartree-Fock dynamics as the number of particles
goes to infinity.

Résumé : We study energy and particle transport for one-dimensional strongly interacting bosons through a single channel connecting two atomic reservoirs. We show the emergence of particle- and energy-current separation, leading to the violation of the Wiedemann-Franz law. As a consequence, we predict different time scales for the equilibration of temperature and particle imbalances between the reservoirs. Going beyond the linear spectrum approximation, we show the emergence of thermoelectric effects, which could be controlled by either tuning interactions or the temperature. Our results describe in a unified picture fermions in condensed matter devices and bosons in ultracold atom setups. We conclude discussing the effects of a controllable disorder.

Résumé : Kondo effect (KE) is omnipresent and universal phenomenon arising in situations where a nanoobject with internal degrees of freedom interacts with a Fermi sea. Starting with brief history of evolution of KE from metals doped with magnetic impurities to complex quantum dots, we concentrate on its realizations in ultra-cold Fermi gases in optical lattices. These systems give unique possibility of achieving overscreening non-Fermi liquid regime for KE, which is highly elusive in other situations where the multichannel KE is the source of Kondo screening.

Résumé : In this talk I will present the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work was motivated by a recent experiment [1], which studied the same system, in the complementary regime of weak interactions.
Based on extensive density matrix renormalization group simulations and a bosonization analysis, we have fully explored the parameter space spanned by filling, inter-leg tunneling, and flux.
As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns and study their dependence on model parameters.

Résumé : The recent impressive experimental progress in the field of quantum simulation paved the way to address the out-of-equilibrium dynamics of many-body systems with an unprecedented degree of control and tunability. Particularly suitable candidates in this respect are cold atoms in optical lattices and arrays of coupled QED cavities.
I will provide an excerpt of my recent theoretical results on the non-equilibrium quantum physics and quantum transport, in both closed and dissipative systems. I will put emphasis on the short- and the long-time dynamics after a sudden quench, emphasizing how strong local correlations between quantum objects are able to non-perturbatively drive the system's behavior. Moreover, I will highlight how the presence of dissipation, naturally driving
the system under non-equilibrium conditions, may drastically change the scenario.

Résumé : In this talk I will present an overview of two exciting, and rather different, recent applications
of entanglement in the study of quantum many-body systems, inspired by the formalism of "tensor networks" and their potential use in quantum computing. I will show that entanglement provides a way to understand the topologically-ordered phases of matter with exotic anyon excitations,
such as those arising in the context of the fractional quantum Hall effect. Here entanglement acts as a link
between conformal field theory, solvable models, and the "matrix-product state" formalism that enables
efficient computational studies of these systems. In the second example, I will illustrate the role of entanglement
in understanding the properties of "many-body localized" phases that have attracted some
attention recently as a novel class of ergodicity-breaking phases that fail to thermalize. It will be shown
how entanglement helps us understand the emergent local integrals of motion which characterize the many-body localized phases and strongly constrain their non-equilibrium dynamics, perhaps leading to possible applications as platforms for "quantum memories".

Résumé : The electronic transport trough a tunnel junction (normal, magnetic or
superconducting) is affected by its electromagnetic environment. The hallmark of
such an interaction is the Dynamical Coulomb Blockade (DCB), a quantum
phenomenon associated with the activation of a Coulomb gap at finite voltage due
to inelastic tunneling processes assisted by the environmental degrees of
freedom [1]. On the other hand, the light emitted into the environment is a
direct witness of the electronic transport, offering an alternative way to
access it [2]. In the first part of the talk, I will study the magnetization
dynamics in ferromagnet|insulator|ferromagnet and
ferromagnet|insulator|normal metal ultra-small tunnel junctions, and
the associated voltage drop in the presence of an electromagnetic environment
assisting the tunneling processes. We find that voltages comparable to the
driving frequency ω can be reached even for small magnetization
precession cone angles θ, in stark contrast to the case where the
environment is absent [3,4]. We stress some possible applications of such an effect, such as the detection of local magnetization precessions in textured
ferromagnets. In the second part, we investigate the properties of the light
emitted by a voltage-biased Josephson junction coupled to a specific
electromagnetic environment [2,5,6]. We show that depending on the particular
implementations [2,6], the resulting photons emitted by the junction can show
pronounced non-classical behavior that is quantified by the second-order
photonic correlation function g2(τ). We calculate explicitly the
g2(τ) function in different limits, and point out that our theoretical
results are in very good agreement with the recent experimental work in Ref.
[6]. Finally, we discuss some further theoretical and experimental extension of
our work such as the production and detection of photonic squeezed states and
photonic entanglement.

Résumé : We evaluate Renyi entropy flows from generic quantum heat engines (QHE) to a weakly-coupled probe environment kept in thermal equilibrium. We show the flows are determined by two quantities: heat flow and fictitious dissipation that manifest the quantum coherence in the engine. This pertains also the common Shanon entropy flow. The results appeal for revision of the concept of entropy flows in quantum non-equilibrium thermodynamics.

Résumé : The last few years have seen a growing experimental
and theoretical activity aiming at extending the simulation
potential of cold atoms to transport properties.
In this presentation, I will show how one can benefit from the
high tunability of cold atom setups to engineer optimal transport
properties. In this framework, I will discuss the proposal and
experimental realization of the investigation of thermoelectric
effects with ultracold atoms, and the possibility to use well
designed transport properties to cool Fermi gases deep into the
degeneracy regime.

Résumé : In the presence of even weak amounts of disorder, low dimensional topological band insulators turn into topological Anderson insulators (tAI). Translational invariance being absent, the tAI must be described by concepts different from the clean limit band structures classification schemes. In this talk we argue that much of the universal physics of the tAI is contained in the system size dependent flow of two parameters, the first of which is an average transport coefficient (at any finite size, the tAI is a conductor), and the second the mean value of a now statistically distributed topological index. These two parameters exhibit flow similar to that of the Pruisken-Khmelnitskii flow diagram of the quantum Hall insulator. Specifically, the flow describes describes quantum criticality at topological phase transitions, the approach towards an insulating configuration away from criticality, and, along with it, the emergenece of a self averaging integer index. For some symmetry classes, that flow can be established in closed analytic form. However, we argue that the overall picture is of more general validity and provides a unified framework to describe both the bulk and the surface physics of the topological Anderson insulator.

Résumé : In the first part of the talk, we study the competition between magnetic and
spin-liquid phases in the Hubbard model on the anisotropic triangular lattice,
which is described by two hopping parameters in different spatial directions,
and is relevant for layered organic charge-transfer salts and for the inorganic
compounds Cs2CuBr4 and Cs2CuCl4.[1,2] By using variational wave functions which
include both Jastrow and backflow terms, we provide solid evidence that two
spin-liquid phases are stabilized in the strongly correlated regime, while
states with spiral magnetic order and a non trivial pitch vector are found close
to the isotropic point. Two different kinds of collinear orders are found in a
wide region of the phase diagram close, respectively, to the limits of square
lattice and decoupled one-dimensional chains. We also introduce another family
of organic charge-transfer salts where a fully anisotropic triangular-lattice
description produces importantly different results, including a significant
lowering of the critical U of the spin-liquid phase.[3]

In the second part of the talk, we consider the extended Hubbard model on the
isotropic triangular lattice as a function of filling and interaction strength.
The complex interplay of kinetic frustration and strong interactions leads to
exotic phases where charge order, antiferromagnetic order, and metallic
conductivity can coexist. Our variational Monte Carlo simulations show that
three kinds of ordered metallic states are stable as a function of
nearest-neighbor interaction and filling. In one of the phases, the coexistence
of conductivity and order is explained by a separation into two functional
classes of particles: part of them contributes to the stable order, while the
other part forms a partially filled band on the remaining substructure.[4]

Résumé : In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte-Carlo procedure from sampling paths that cause the many-body density
matrix to change sign. Unfortunately, this high-dimensional nodal surface is
not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperature path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems.

Résumé : The non-interacting topological insulators (TIs) have attracted great
interest in the last decade. While this class of materials is today
well-understood, the effect of electron-eletron interactions in such
systems remains in general elusive. In this talk, I will address and
discuss two different aspects of interactions in 2D topological band
structures: (i) in some cases, strongly interacting TI models can be
used to describe the exotic magnetic properties of certain transition
metal oxides. (ii) in other cases, strong interactions can drive a TI into
spin-liquid phases.

Résumé : Feshbach resonances - namely resonances between an unbound two-body state (atomic state) and a bound (molecular) state - are a unique tool to tune the interaction properties of ultracold atoms. In this talk, I will show that the coherent coupling of the atomic and molecular state, can lead to a novel insulating phase - the Feshbach insulator - for bosons in an optical lattice close to a narrow Feshbach resonance. This new state of quantum matter appears around the resonance, preventing the system from collapsing when the effective atomic scattering length becomes negative.
Surprisingly enough, the transition from condensate to Feshbach insulator has a characteristic first-order nature, due to the simultaneous loss of coherence in the atomic and molecular components.
Our realistic study shows that these features appear clearly in the ground-state phase diagram of e.g. rubidium 87 around the 414 G resonance, and they are therefore directly amenable to experimental observation.

Résumé : Quasicrystals can be modelled with a collection of polygons (tiles) that
cover the whole plane, so that
each pattern (a sub-collection of tiles) appears up to translation with
a positive frequency, but the tiling is not periodic. The frequency of
presence of each pattern determines the spectrum of the system, and this
is the subject of the gap labelling theory [1].

Using a microwave realization of a tight-binding Penrose-tiled
quasicrystal [2], we measured the gap labelling and the spatial energy
distribution of each eigenstate [3]. The energy-scaling behaviour of the
hopping terms in this particular system, allowed us to identify the main
patterns that determine the first hierarchical structure of the spectrum
. Our energy-scaling analysis enabled us not only a straightforward
interpretation of the gap labelling but also a full understanding of the
wavefunction behaviour observed in each band.

The next goal will be the realization of a light Penrose-tiled
quasicrystal for ultracold atoms, the underlying idea being to have
access to samples with a lager number of tiles and thus to have the
opportunity to observe the hierarchical effect of larger and larger
patterns in the gap labelling. We have shown that this may be possible
by mapping the gap labelling on a Brillouin zone (BZ) labelling and
measure the areas of the extended BZs or the Bragg peak intensity
distribution via different time-of-flight techniques [4].

Résumé : In this talk I will show some applications of the Time Dependent Density Functional Theory and Many Body Perturbation Theory (GW/BSE) on molecular systems of technological and biological interest (natural dyes, retinal chromophore, Peridinin carotenoid), focusing on the effects of intrinsic structural fluctuations and environment (solvent, protein) on their optical properties.
I will illustrate how these effects dramatically affect the absorption spectra of these systems, and how they can be reasonably taken into account in TDDFT and MBPT framework via multi-scale techniques or hybrid quantum-classical approximations using quantum Monte Carlo(QMC) method for the structural properties and the Bethe Salpeter equation to simulate the excitations of these molecules in their "natural” environment.

Résumé : A first-principles implementation of the Kadanoff-Baym Equation (KBE)
for extended systems is presented. The KBE describes both the carriers
dynamics and the polarization dynamics by means of the
out-of-equilibrium Green’s function [1]. When the polarizarion is
considered, the inclusion of the static self-energy and the changes in
the time-dependent Hartree potentials
give, in the linear regime limit, the time dependent extension of the
well-known Bethe-Salpeter equation [2]. These effects also ensures a
correct coupling between the electronic system and the laser pulse,
that is between the field intensity and the number of electrons
injected in the conduction band. The terms describing the dynamical
correlation instead, also known as scattering terms, are the key
players in the relaxation process. In our approach they are included
within the out of equilibium extensions of the GW, for the
electron-electron interaction, and FAN, for the electron-phonon
interaction self-energy [3].
In particular we describe how equilibrium is restored in bulk Silicon,
when carriers are injected in the conduction band by an ultra-short
laser pulse. The excited electrons and holes relax towards two Fermi
distributions, within about one hundred femtoseconds. While the two
Fermi distributions are created the energy gained by the electronic
system is dissipated to the lattice. The whole process is completed on
the pico-seconds time-scale. The correct balance between the
electronic and the phononic scattering processes is obtained thanks to
a double grid sampling of the Brillouin zone. The results of the
simulations are also compared with recent pump-probe measurments with
femtosecond laser pulses [4–7]

Résumé : Matter occurs in various phases with different properties. Usually these phases are characterized in terms of symmetry breaking. A major discovery in the 1980s was the quantum Hall effect which forms a new kind of “topological” order. This order represents exotic phases with unusual properties and cannot be understood in terms of symmetry breaking. Since then, a growing number of instances of topological phases has accumulated, and important applications – not least topological quantum computers – have been proposed, but a characterization and classification of these new phenomena has been slow to emerge. In parallel, DMRG has arrived as a powerful numerical method with ex- tensions to two dimensional systems and time-dependent phenomena. I will show how to use DMRG to develop new frameworks that help to understand topologically ordered systems. For example, it is now possible to extract characterizing properties of the anyonic excitations di- rectly from the ground state of fractional quantum Hall systems. This approach further makes contact with “measurable” quantities (Hall viscosity) and field theories (central charge at critical points). Other remarkable examples are symmetry protected topological phases in one-dimensional systems for which DMRG provides a complete characterization.

Résumé : The new challenges posed by the need of finding strong rare-earth free magnets
demand methods that can predict magnetization and magnetocrystalline anisotropy
energy (MAE). In this talk, I will review the general status of electronic
structure approaches to this problem. I will then argue that correlated electron
effects, which are normally underestimated in band structure calculations, play
a crucial role in the development of the orbitalcomponent of the magnetic
moments. Because magnetic anisotropy arises from this orbital component, the
ability to include correlation effects has profound consequences on our
predictive power of the MAE of strong magnets. I will show that incorporating
the local effects of electronic correlations with dynamical mean-field theory
provides reliable estimates of the orbital moment, the mass enhancement and the
MAE of YCo5.

Résumé : Mesons are bound states of a quark and an antiquark. The four neutral
mesons B_d, B_s, D, and K have the unique property that they mix with
their antiparticles. This means that a meson-antimeson system
forms a quantum-mechanical two-state system, exhibiting the familiar
oscillations between the two states. These neutral meson sytems are
gold mines for the study of the CP symmetry, which links the
interactions of particles to those of antiparticles. Since 1964 it is
known that CP is violated and today CP asymmetries are
experimentally studied with high precision. These investigations might
reveal new laws of nature well ahead of collider experiments which aim
at the production of new particles in high-energy collisions.

Résumé : The development of solar cells is driven by the need for clean and sustainable
energy. Organic and dye sensitized cells (DSC) are considered as promising
alternatives for traditional single crystal silicon cells, particularly for
large area, low cost applications. However, the efficiency of such cells is
still far from the theoretical limit.
First-principles quantum mechanical simulations may be used for computer-aided
design of new materials, material combinations, and nano-structures for more
efficient organic and dye-sensitized cells. To this end, it is important to
obtain an accurate description of the electronic structure, including the
fundamental gaps and energy level alignment at interfaces. This requires a
treatment beyond ground-state density functional theory (DFT). Within the
framework of many-body perturbation theory (MBPT), these properties may be
calculated using the GW approximation, where G is the one-particle Green's
function and W is the dynamically screened Coulomb potential.
In this talk I will provide an introduction to GW methods and demonstrate their
applications to the components of organic and dye-sensitized solar cells: TiO2
clusters [1], organic semiconductors [2,3], dyes [4,5], and dye-sensitized TiO2
clusters [6,7].

Résumé : Ferroelectricity in ABO3 perovskites and related compounds has been a topic of intensive research for more than 60 years. Recently, the coupling of the ferroelectric mode with other structural distortions has attracted an increasing interest since it offers promising and still widely unexplored possibilities to couple ferroelectricity with other functional properties and even to produce unusual phenomena. In this context, the trilinear coupling between ferroelectric and oxygen rotational modes in naturally-occuring and artificial layered perovskites emerged as a practical way to produce unusual dielectric properties or to achieve enhanced magneto-electric coupling. Focusing on titanate and vanadate systems, we will discuss here how even more exciting new phenomena can appear when additional orbital and charge orders enter into play!

Résumé : In most systems that exhibit order at low temperatures, the order occurs in the elementary degrees of freedom such as spin or charge. Prominent examples are magnetic or superconducting states of matter. In contrast, emergent order describes the phenomenon where composite objects exhibit longer range correlations. Such emergent order has been suspected to occur in a range of correlated materials. One specific example are spin systems with competing interactions, where long-range discrete order in the relative orientation of spins may occur. Interestingly, this order parameter may induce other phase transitions as is the case for the nematic transition in the iron pnictides. In this talk, we introduce and discuss a system with emergent Z6 symmetry, a two-dimensional frustrated Heisenberg antiferromagnet on the windmill lattice consisting of interpenetrating honeycomb and triangular lattices [1,2]. The multiple spin stiffnesses can be captured in terms of a four-dimensional metric tensor, and the renormalization group flow of the stiffnesses is described by the Ricci flow of the metric tensor. The key result is a decoupling of an emergent collective degree of freedom given by the relative phase of spins on different sublattices. In particular, our results reveal a sequence of two Berezinskii-Kosterlitz-Thouless phase transitions that bracket a critical phase.

Résumé : Upon application of an external tuning parameter, a magnetic state can be driven
to a normal metal state at zero temperature. This phenomenon is known as quantum
criticality and leads to fascinating responses in thermodynamics and transport
of the compound. In the standard picture, a single quantum critical point occurs
at zero temperature, which results in a nontrivial critical behaviour in its
vicinity. Here we show that in two dimensions the scenario is considerably more
complex due to the enormous amount of quantum fluctuations. Instead of the
single point separating the antiferromagnet from the normal metal, we have
discovered a broad region between these two phases where the magnetic order is
destroyed but certain areas of the Fermi surface are closed by a large gap. This
gap reflects the formation of a novel quantum state characterised by a
superposition of d-wave superconductivity and a quadrupole-density wave, id est
a state in which an electron quadrupole density spatially oscillates with a
period drastically different from the one of the original spin-density wave. At
moderate temperatures both orders co-exist at short distances but thermal
fluctuations destroy the long-range order. Below a critical temperature the
fluctuations are less essential and superconductivity becomes stable. This new
phenomenon may shed some light on the origin of the mysterious pseudogap state
and of the high-temperature transition into the superconducting state in
cuprates. Our results demonstrate that quantum phase transitions between
antiferromagnets and normal metals in layered materials may be the proper
playground for search of new high temperature superconductors.

Résumé : Quantum annealing - a finite temperature version of the quantum adiabatic algorithm - combines the classical technology of slow thermal cooling with quantum mechanical tunneling, to try bring a physical system towards its ground state. The Canadian company D-Wave systems has recently built and sold programmable devices that are designed to use this effect to find solutions to hard optimization problems. I will present results of experiments designed to shed light on crucial questions about these controversial devices: are these devices quantum or classical? Are they faster than classical devices? What is their potential?

Résumé : Helical edge states are the electronic conducting states emerging at the
boundaries of a 2D topological insulator, which are currently under the
spotlight due to their peculiar properties. These channels are characterized by
a tight connection between the electron group velocity and the spin orientation,
and exhibit a perfect transmission, as recently observed in CdTe/HgTe and
InAs/GaSb quantum wells. When a constriction is realized in the 2D quantum
well, electron tunneling between helical edge states occurs via two types of
channels allowed by time-reversal symmetry, namely spin-preserving (p) and
spin-flipping (f) tunneling processes. Determining and controlling the effects
of these two channels is crucial to the application of helical edge states in
spintronics. We show that, despite the Hamiltonian terms describing these two
processes do not commute, the scattering matrix entries of the related
4-terminal setup always factorize into products of p-terms and f-terms
contributions. Such factorization provides an operative way to determine the
transmission coefficient Tp and Tf related to each of the two processes, via
transconductance measurements.
Furthermore, these transmission coefficients are also found to be controlled
independently by a suitable combination of two side gate voltages applied
across the junction. This result holds for an arbitrary profile of the tunneling
amplitudes, including disorder in the tunnel region, enabling us to discuss the
effect of the finite length of the tunnel junction, and the space modulation of
both magnitude and phase of the tunneling amplitudes.

Résumé : We investigate the dynamics of a critical XXZ spin-1/2 chain prepared in an inhomogeneous initial state with different magnetizations on the left and right halves. We simulate the real-time evolution using the time-evolving block decimation (TEBD) method. We follow the front propagation by measuring the magnetization and entanglement entropy profiles, and we focus on the situation where the initial state is not fully polarized. At long times, as in the free fermion case (T. Antal et al. 1999), a large central region develops where correlations become time-independent and translation invariant. The shape and speed of the fronts is studied numerically and we evaluate the stationary current as a function of initial magnetic field and as a function of the anisotropy \Delta. We compare the results with the conductance of a Tomonaga-Luttinger liquid, and with the exact free-fermion solution at \Delta=0. We also investigate the two-point correlations in the stationary region and find a good agreement with the "twisted" form obtained by J. Lancaster and A. Mitra (2010) using bosonization. Some deviations are nevertheless observed for strong currents.

Résumé : In this talk I will focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting and (ii) proximity coupled Rashba wires. In particular, I will discuss how, while being detrimental to the topological order in p-wave wires, the disorder can {it induce} topological state in Rashba wires contrary to common expectations. The total phase space area of the topological state is conserved for long disordered wires, and can even be increased in an appropriately engineered superlattice potential. I will also discuss how, in finite wires, the Majorana state oscillates as a function of chemical potential and magnetic field. I will conclude with a discussion of recent experiments, which was conducted on dirty Rashba wires, in the light of these new results.

Résumé : We present an accurate method to determine ground-state properties
of strongly-correlated electrons decribed by lattice-model Hamiltonians.
In lattice density-functional theory (LDFT) the basic variable is the
one-particle density matrix $gamma$. From the HK theorem,
the ground state Energy $E_{gs}[gamma_{gs}] = min_{gamma} E[gamma]$
is obtained by minimizing the energy over all the representable $gamma$.
The energy functional can be divided into two contributions:
the kinetic-energy functional, which linear dependence on $gamma$ is
axactly known, and the correlation-energy functional $W[gamma]$,
which approximation constitutes the actual challenge.
Within the framework of LDFT, we develope a numerical approach to
$W[gamma]$, which involves the exact diagonalisation of an effective
many-body Hamiltonian of a cluster surrounded by an effective field.
This effective Hamiltonian depends on the density matrix $gamma$.
In this talk we discuss the formulation of the method and its
application to the Hubbard and single-impurity Anderson models
in one and two dimensions. The accuracy of the method is
deponstrated by comparison with the Bethe-Ansatz solution (1D),
density-matrix renormalization group calculations (1D),
and quantum Monte Carlo simulations (2D).

Résumé : We study [1,2] the tunneling density of states (TDOS) of a disordered electronic
system with Coulomb interaction on both the metallic and insulating sides of an
Anderson-localization metal-insulator transition (MIT). We discuss how the
zero-bias anomaly on the metal side transforms into the Coulomb-gap suppression
of the TDOS in the localized phase of the MIT. For tunneling into the insulating
phase, the average TDOS shows a critical behavior at high energies, with a
crossover to a soft Coulomb gap Δ at low energies. We demonstrate that the
single-particle excitations experience a localization transition (which belongs
to the noninteracting universality class) at an energy E=±Ec. The mobility edge
Ec scales with the distance μc−μ from the interacting critical point according
to Ec∝(μc-μ)nu z, where nu and z are the interacting localization-length and the
dynamical critical exponents. Our theoretical expectations and the "phase
diagram" of the Anderson MIT in the presence of Coulomb interaction are in an
overall agreement with recent experimental results [3] for the average TDOS in a
device with a tunable doping level across the MIT.

We further explore mesoscopic fluctuations and correlations of the local density
of states (LDOS) near the MIT. It is shown that the LDOS multifractality
survives in the presence of Coulomb interaction. Specifically, the LDOS shows
strong fluctuations and long-range correlations which reflect the
multifractality associated with interacting and noninteracting fixed points as
well the localization of low-energy excitations. By using the onlinear
sigma-model approach, we calculate the spectrum of multifractal exponents of a
Coulomb-interacting system without time-reversal and spin symmetries in 2+ϵ
spatial dimensions and show that it differs from that in the absence of
interaction. The multifractal character of fluctuations and correlations of the
LDOS can be studied experimentally by scanning tunneling microscopy of
two-dimensional and three-dimensional disordered structures. Our results are in
an overall agreement with the experimental data of Ref. [4]. In addition to MIT
and transitions between different phases of topological insulators, we envision
a possibility to extend our analysis also to superconductor-insulator
transitions.

Résumé : The quantum coherence effects between electrons in nanodevices lead to a
rich variety of phenomena in quantum transport. One of these is the
violation of Kirchhoff's laws in the quantum RC-circuit. In this system,
a metallic lead exchanges electrons coherently with a quantum dot driven
dynamically by a top metallic gate. In the non interacting case,
the charge relaxation resistance of the system differs from the usual
dc-transport resistance given by the Landauer formula. The charge
relaxation resistance is universally fixed to h/(2e2) for a single mode
conductor, regardless of the transmission of the mode. I will show that
the Fermi liquid behavior of these systems at low energy explains this
universality even in the presence of strong interactions in the dot.
Moreover, I will discuss the emergence of a giant dissipation regime
associated to the breaking of the Kondo singlet for Zeeman energies of
the order of the Kondo temperature. I will provide a comprehensive
analytical description of the peak of the charge relaxation resistance
associated to this giant dissipation and demonstrate its persistence out
of the Kondo regime.

Résumé : In one and two spatial dimensions there is a logical possibility
for identical quantum particles different from bosons and fermions, obeying
intermediate or fractional (anyon) statistics. I will consider applications
of recent bounds for the energy of a many-particle wave function in terms
of its density, so called Lieb-Thirring inequalities, to models of anyons
in two dimensions, as well as to models in one dimension of Lieb-Liniger
and Calogero-Sutherland type. These bounds follow from a local form of the
exclusion principle valid for such generalized exchange statistics modeled
by interactions. This is joint work with Jan Philip Solovej.

Résumé : A phenomenological analysis of resistance and diamagnetic response in the
LaAlO3/SrTiO3 or LaTiO3/SrTiO3 (LXO/STO) heterostructures suggests the
occurrence of a low-dimensional (e.g., filamentary or fractal) structure of the
superconducting cluster with small long-distance connectivity embedded in the
two-dimensional system [1,2]. To explain the systematic occurrence of such
mesoscopically disordered regions, we model the electron gas at the interface of
oxide heterostructures considering a twodimensional electron gas in the presence
of a sizable Rashba spin-orbit coupling (RSOC). Under simple general
assumptions, we show that an electronic phase separation occurs for realistic
values of the RSOC and of the band parameters [3,4]. This could provide an
intrinsic mechanism for the recently observed inhomogenous phases at the LAO/STO
or LTO/STO interfaces and opens the way to new interpretations of the quantum
critical behaviour of LTO/STO [5]. We investigate the effects of temperature and
magnetic field on the charge instability finding a novel type of quantum
critical point related to the vanishing of the critical temperature of the
electronic phase separation [4].

Résumé : Over the last few years, there has been an upsurge of interest in materials
in which exotic states may emerge as the result of relativistic spin-orbit
interactions. We will discuss insulating iridium oxides from this perspective.
We show that the strong spin-orbit coupling, through the entanglement of spin
and orbital spaces, leads to a variety of interesting Hamiltonians ranging
from the Heisenberg model to the Kitaev or quantum compass models,
for different lattice geometries [1]. Based on these effective
Hamiltonians, we present a comprehensive theoretical study [3,4] of the rich
phase behavior and dynamics observed in layered iridium oxides such as
tetragonal Sr2IrO4 and Sr3Ir2O7 and hexagonal A2IrO3 (A=Na, Li).
We suggest that the hexagonal iridates might be close to the
Kitaev spin-liquid state. We also discuss the layered tetragonal vanadate
Sr2VO4 and argue that magnetically-hidden octupolar order, driven
by spin-orbit coupling, is realized in this compound [2].

Résumé : In this talk I will focus on passive and active motion in blood suspension and other suspensions. I will first discuss how to model blood flow from microscopic considerations (i.e. by taking blood element explicitly into account, e.g. red blood cells). I will show some dynamics of individual red blood cells, and then present collective dynamics and some intringuing rheological behaviors in microcirculation. I will then discuss some issues related to the so-called ameboid swimming. Microorganisms, such as bacteria, algae, or spermatozoa, are able to propel themselves forward thanks to flagella or cilia activity. By contrast, other organisms employ pronounced changes of the membrane shape to achieve propulsion, a prototypical example being the Eutreptiella gymnastica. Cells of the immune system as well as dictyostelium amoebas, traditionally believed to crawl on a substratum, can also swim in a similar way. A model will be presented and it will be shown that fast propulsion can be achieved with adequate shape adaptations. The autopropulsion distance over one cycle is a universal linear function of a simple geometrical dimensionless quantity A/V^(2/3) (V and A are the cell volume and its membrane area). This study captures the peculiar motion of Eutreptiella gymnastica with simple force distribution.